KdV–Burgers equation in the modified continuum model considering anticipation effect

•The driver’s anticipation effect is introduced into the OV car-following model•The KdV–Burgers equation and one solution are obtained, which is seldom investigated•Numerical simulation is made to show the local cluster described by the model

The new continuum model mentioned in this paper is developed based on optimal velocity car-following model, which takes the drivers’ anticipation effect into account. The critical condition for traffic flow is derived, and nonlinear analysis shows density waves occur in traffic flow because of the small disturbance. Near the neutral stability line, the KdV–Burgers equation is derived and one of the solutions is given. Numerical simulation is carried out to show the local cluster described by the model.